Non-destructive design around a circle/cylinder
I don't know if you can do it with curves and full non-destructive, but here is a way to do it with mesh and destructive...  ;)


Create your wave profile.
Bend it 360° with the Simple Deform modifier / Bend mode.
Give your object a Solidify modifier.
Give it a Bevel modifier / Angle mode so that the angles will be sharp when you'll add the Subdivision Surface modifier. You might prefer a Bevel / Weight mode if you want to have a different bevel on top and bottom. Or add some edge loops instead of Bevel modifier.
Add a Subdivision Surface modifier to smooth your object, also, smooth it with Smooth shading option.
It looks like you can't avoid the seam where the 360° shape joins, so I guess you need to apply the Simple Deform modifier.
Once you've done it, remove the doubles so that it joins properly.
Link-duplicate the ring with altD.
Rotate this copy 180° on the Y axis.
Create the inner ring.